On a horizontal pipe with a diameter of 100 mm, having a narrowing d = 40 mm, water moves in an amount of 6 l / s Determine the pressure in a narrow section if the water pressure before the narrowing is (Z 1) m. neglect the pressure loss.
Given: D = 100mm = 0.1m; d = 40mm = 0.04m; Q = 6l / s = 0.006m / s; H = (Z 1) = 2 1m
 
Figure 1 - Pipe scheme
Decision

1. We write the equation of continuity of flow for sections 1-1 and 2-2
                                             (one)
where Q is the flow rate through sections 1-1 and 2-2; V1, V2 - water velocity in section 1-1 and 2-2; ω1, ω2 - sectional area 1-1 and 2-2; D, d is the diameter of the pipeline in sections 1-1 and 2-2.
From ur-ia (1) we find the velocities in sections
                                        (2)
                                        (3)
2. We write the Bernoulli equation for an ideal fluid for sections 1-1 and 2-2:
                                   (2)
where z1, z2 is the geometric pressure in section 1-1 and 2-2, m; p1, p2 — fluid pressure in sections 1-1 and 2-2, Pa; v1, v2 — flow velocity in sections 1-1 and 2-2, m / s; ρ is the density of the liquid, kg / m3; H-pressure in section 1-1.
The geometric height in the sections z1 = z2 = 0, because the pipe is horizontal.
Express from (2) the pressure in a narrow section 2-2
  
                   (four)
3. Determine the pressure in a narrow section
 

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